Chapter 6.1, Problem 57E

To determine

To calculate:

Given logarithm using change of base formula.

Answer to Problem 57E

Simplified form of given logarithm is ${\log }_{4}7=1.403$

Explanation of Solution

Given information:

  ${\log }_{4}7$

Calculation:

Consider the given logarithm,

  ${\log }_{4}7$

Let $a$ and $x$ be two positive real numbers such that $a\ne 1$ then ${\log }_{a}x$ can be converted to the base $10$ as below:

  $\log x=\frac{\log x}{\log a}$

By using above formula solve the expression,

  $\begin{array}{l}{\log }_{4}7=\frac{\log 7}{\log 4}\\ =\frac{0.845}{0.602}\\ =1.403\end{array}$

Hence, simplified form of given logarithm is ${\log }_{4}7=1.403$